eTA and ESTA
First things first, you will need a passport to be requested in the offices of your country of origin, and once obtained, you need to apply for getting the documents needed to enter the two countries, Canada and the United States, by filling in the appropriate online forms in the governed sites of the two countries, the eTA and ESTA application for Canada and the United States respectively. I invite you to read all the information on the websites and to pay close attention, as for there are more stringent procedures for some countries and sometimes eTA and ESTA may not be enough for access to the territories.
I proceed very schematically in this case trying to answer your questions.
When did you travel?
The flights I booked were intended from 7 of 22 of August, with arrival to Toronto and departure from New York. Traveling in August is more expensive, but it’s the only time of the year in which I am allowed to leave for longer periods. Obviously if you have the opportunity to travel at other times of the year, consider it carefully since flights are way cheaper.
How far in advance should I book a flight?
Earlier you book, the less you pay. I would say that seven or eights months in advance should be fine to get the best price. I personally have booked five months before the date of the flights concerned and I have payed a bit more, so I suggest to hurry up.
Where do you look for flights?
I recommend reading my post on where I look for flights.
As for the first shift from Toronto to Montreal, I traveled with Megabus, the American Flixbus, a little more disorganized but functional and above all very convenient, since you can move from Ontario to Quebec with only 10 dollars. As for the route from Montreal to New York, I flew with Air Canada: a one-hour, quick and easy trip.
Now I hardly use anything else but Airbnb to book my accommodations when I travel, and I suggest you to do the same (even to save money) especially in North America, a place where the platform is very developed. My advice is to always choose a staying which is closer to the center, since all three are huge cities and moving around each of them becomes a trip by itself sometimes, especially in New York, where 20 to 30 minutes on the subway are the average way to move, even just on the island of Manhattan.